In this article, we use the Hausdorf distance to treat triple Simpson’s rule of Henstock integral a fuzzy valued function as well error bound method. We also introduce δ-fine subdivisions for and numerical example is presented in order show application consequence

We prove two existence theorems for the integrodifferential equation of mixed type: x′(t) = f (t,x(t), t0k1(t,s)g(s,x(s))ds, ∫ a 0k2(t,s)h(s,x(s))ds), x(0) = x0, where in the first part of this paper f , g, h, x are functions with values in a Banach space E and integrals are taken in the sense of Henstock-Kurzweil (HK). In the second part f , g, h, x are weakly-weakly sequentially continuous fu...

In this paper we introduce and investigate a Henstock-Kurzweil-type integral for Riesz-space-valued functions defined on (not necessarily bounded) subintervals of the extended real line. We prove some basic properties, among them the fact that our integral contains under suitable hypothesis the generalized Riemann integral and that every simple function which vanishes outside of a set of finite...

In this paper, we give sufficient conditions for the existence and uniqueness of solution Sturm–Liouville equations subject to Dirichlet boundary value involving Kurzweil–Henstock integrable functions on unbounded intervals. We also present a finite element method scheme functions.